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What Are the Odds?

As a physicist at California Institute of Technology and the author of many books and articles, a number of them on the science of probability, Leonard Mlodinow spends a lot of time considering the question, What are the odds?

For instance, what are the odds that a single person might write — as Dr. Mlodinow has — a paper titled “Pseudo-spin Structure and Large N Expansions for a Class of Generalized Helium Hamiltonians,” a best-selling book with Stephen Hawking and at least one episode of “McGyver.” (Answer: Pretty low.)

Dr. Mlodinow has a particular, and personal, interest how the most painful events can sometimes yield unexpected results. In the first chapter of his best-seller, “The Drunkard’s Walk: How Randomness Rules Our Lives,” he writes of a conversation with his father, who tells him of how he came to survive his time in the concentration camp in Buchenwald:

It struck me then that I have Hitler to thank for my existence, for the Germans had killed my father’s wife and two young children, erasing his prior life. And so were it not for the war, my father would never have emigrated to New York, never have met my mother, also a refugee, and never have produced me and my two brothers … The outline of our lives, like the candle’s flame, is continuously coaxed in new directions by a variety of random events that, along with our responses to them, determine our fate.

He answered the following questions via e-mail:

An earlier post by the psychologist Daniel Gilbert makes the argument that uncertainty — not knowing what misfortune will come — makes people more unhappy than misfortune itself. Do you find that to be true?

It does seem to be true of my own psychology. Also, I find that what’s most important, whatever happens, is how you deal with it. And once something bad actually happens, you can start that process, and bad can eventually even turn into good.

Many people are understandably anxious and depressed about their present and future situations. Based on what you know about predictions and human behavior, should they be?

I find that predicting the course of our lives is like predicting the weather. You might be able to predict your future in the short term, but the longer you look ahead, the less likely you are to be correct. In my own life, many things that seemed to be very bad at first actually had good consequences. For example, just as I had begun making a living writing in Hollywood many years ago, the Writer’s Guild called a strike. I thought it was awful for my fledgling career, not to mention financially ruinous. But as it turned out, the strike gave busy producers a chance to catch up on their reading, and the day the strike ended I got a call from the show runner at “Star Trek: the Next Generation,” who said he read a “McGyver” script of mine he had found lying around, loved it, and wanted to hire me on the show’s writing staff. It was a plum job and a boost to my career, and it would have never happened if not for the strike.

So I try to relax, and work on making the best of whatever develops, rather than worrying about how awful it is.

In times of crisis, such as this one, are most people able to accurately predict the outcomes of situations? Or do they tend toward too much optimism or too much pessimism?

“As someone who has taken risks in life I find it a comfort to know that even a coin weighted toward failure will sometimes land on success.”

I don’t think complex situations like this one can be predicted. There are too many uncontrollable or unmeasurable factors. Afterwards, of course, it will appear that some people had gotten it just right: since there are many people making many predictions, no doubt some of them will get it right, if only by chance. But that doesn’t mean that, if not for some unforeseen random turn, things wouldn’t have gone the other way.

The social historian (and socialist) Richard Henry Tawney, wrote, “Historians give an appearance of inevitability… by dragging into prominence the forces which have triumphed and thrusting into the background those which they have swallowed up.” And the (neo)conservative historian Albert Wohlstetter said it this way: “After the event, of course, a signal is always crystal clear. We can now see what event the disaster was signaling … but before the event it is obscure and pregnant with conflicting meanings.”

In some sense this idea is encapsulated in the cliché that “hindsight is always 20/20,” but people often behave as if the adage weren’t true. In government, for example, a “should-have-known-it” blame game is played after every tragedy. In the case of Pearl Harbor, for example, seven committees of the United States Congress delved into discovering why the American military had missed all the “signs” of a coming attack. One of the pieces of evidence cited as a harbinger recklessly ignored by the U.S. Navy was a request, intercepted and sent to the Office of Naval Intelligence in Washington, that a Japanese agent in Honolulu divide Pearl Harbor into five areas and make future reports on ships in harbor with reference to those areas. Of special interest were battleships, destroyers and carriers, as well as information regarding the anchoring of more than one ship at a single dock. In hindsight , that sounds ominous, but at other times similar requests had gone to Japanese agents in Panama, Vancouver, Portland and San Francisco. [The analysis is most famously laid out in the 1963 book, “Pearl Harbor: Warning and Decision,” by Roberta Wohlstetter, who was married to Albert, noted above.]

In addition to the intelligence reports that in hindsight seem to point toward a specific attack, there is also a huge background of useless intelligence, each week bringing new reams of sometimes alarming or mysterious messages and transcripts that would later prove misleading or insignificant. In advance of the event, you can’t tell one sort from the other.

It is hard to say whether people are too optimistic or too pessimistic. That depends on the person. But we should keep in mind that it is easy to concoct stories explaining the past, or to become confident about dubious scenarios of the future. We should view both explanations and prophecies with skepticism.

Should emotions — despair, anger, happiness — play a part in the decisions people make in their lives? In other words, should our feelings matter?

Of course our feelings matter. But emotional decisions are usually not the best ones. On the other hand, your emotions can affect your decisions whether you like it or not because the effects can occur on the unconscious level. One study even showed that subjects holding a hot cup of coffee judged people differently than subjects holding a cold cup. In my case, that effect wouldn’t have been unconscious, though. I know that cold coffee makes me grumpy.

A recent news story about treating cancer told the story of one woman — a non-smoking vegetarian who exercised and had little incidence of cancer in her family — who was shocked by her cancer diagnosis. Was her reaction — and others like it — reasonable? Does “living right” work against the odds that illness or misfortune will strike us?

Assuming one is correct about the proper way to “live right” — and I’m not convinced that a straight vegetarian diet is the healthiest — it is possible to decrease the odds of bad outcomes, but that doesn’t mean they won’t occur. Anything that is possible eventually will occur, which means that some healthy-living people will get cancer, and some chain smokers won’t. I once read a story about a church group that was supposed to meet at a certain time. Ten minutes after the appointed time, due to a gas leak, the church blew up. If they had not showed up late, all 10 would have been killed. Some see that as evidence that God was watching over them. Others might conclude that you should always show up to church late. All I learn from that is that it is a big country, and if you ask around enough, you’ll hear some pretty improbable stories.

Another example, which I analyze in “The Drunkard’s Walk,” is the time Roger Maris, a very good but not great player, broke Babe Ruth’s beloved record, hitting 61 home runs in 1961. Maris had never came close to that output before, nor did he after. What happened?

We all know that players will hit a few more home runs than usual in some years, and a few less in others. But the mathematics of chance also predicts that some years they’ll hit a lot more, and some years a lot less. Those large fluctuations are rare, and wouldn’t be record-breaking for most players, in any case. But the historical statistics of baseball show that there were enough players with excellent, but sub-Ruthian, ability that over the years that it was probable that, by chance alone, one of them would have a single standout year in which they tie or break Ruth’s record. In fact, every stand-out record in any sport that has ever been analyzed has always been found to be consistent with the patterns produced by random fluctuations. Performance over time comes mainly from talent and practice. But achievements that stand out from an athlete’s usual performance — hot streaks or record years — happen with patterns that match the patterns of chance. Just wait long enough, and strange things will happen.

Can a full understanding of the probability of certain outcomes help reduce anxiety? For instance: would knowing the statistical frequency (or infrequency) of plane crashes help someone overcome a fear of flying? Would a smoker knowing the actual odds that he will get cancer make him less fearful of that outcome? In short, do we worry too much, or too little?

My mother worries too much. Some say I worry too little. I guess that shows a) that one cannot say “we” worry too much or too little, and b) that whether an individual worries too much or too little is not 100 percent inherited from your mother.

I was once on a plane that experienced so much turbulence that when I looked out the window, the wings seemed to flap up and down like a bird’s. I noticed, also, that the woman in the window seat next to me looked pale and terrified. Personally, I took comfort in knowing how many miles planes fly through heavy turbulence without any problems at all. So I explained to the woman how planes were designed to withstand such conditions, and told her the slim odds of anything bad happening. When I finished, she turned away and reached for the barf bag.

Some people take solace in an understanding of their environment, others don’t. For me, an understanding of the role played by chance has taught me that one important factor in success is under our control: the number of at-bats, the number of chances taken, the number of opportunities seized. As someone who has taken risks in life I find it a comfort to know that even a coin weighted toward failure will sometimes land on success. Or, as I.B.M. pioneer Thomas Watson said, “If you want to succeed, double your failure rate.”

Leonard Mlodinow teaches randomness to future experimenters at Caltech. His books include “The Drunkard’s Walk: How Randomness Rules Our Lives” and “Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace.” More of his writing and information about his work can be found at his Web site.

The point about finding astounding random exceedances is certainly good. People certainly want to believe in apparent patterns in true randomness. But aren’t there truly outstanding practitioners? How does one distinguish them, the Babe Ruths, who were “great”, from the Roger Marises, who were “lucky”? Does this go beyond statistics?

(End of questions.)

This seems to raise a question about the whole American reliance on statistics to judge performance — in any field, including education — instead of looking at how things are done. The Babe and Joe DiMaggio weren’t great because of their numbers, but because of how they played. Simiilarly, we don’t make scientific advances by measuring correlations but by finding out how things work. Statistics can help but they are secondary.

Sixty-five years ago, in my Latin class, I memorized a succinct Latin tag–“Post Hoc Ergo Propter Hoc”. I have tried to remember it and use it, whenever I hear or read about most assertions of uni-causalalaity. So, rather than take uni-causal propositions seriously, I treat them as humorous and yet tragic, tragic if they are acted on inappropriately.
Any Latinists out there are welcome to correct my fading memory of Latin.

My first mentor, psychologist Albert Ellis, recalled that early in his career he had a fear of flying. He experienced high anxiety whenever he flew. His initial efforts to overcome his anxiety involved estimating the odds of a plane crash. Although he figured the odds were high, he still felt severe anxiety when flying, almost to the point of panic. The reason for this, he soon discovered, was because he still held the belief, “The plane absolutely must not crash under any circumstances!” Despite the long odds, he was still demanding certainty. Then, Ellis took a profound philosophic stance and told himself, “If the plane crashes, it crashes! Too bad! And if I die, I die!” It was then and only then that his anxiety disappeared.

The point of this story is that we are living in an uncertain world. Much of what we call anxiety comes from our demand for certainty in an uncertain world, and our “awfulizing” about the consequences of what might happen. Until we confront the worst and accept it — but not like it — we will be needlessly anxious. //www.jeffreyguterman.com

understanding that we do have control of our choices, however not the outcome (as so much of it does have to do with chance — or fate as i tend to believe), for me personally, requires a high level of trust (faith) to replace any fear or worry that would be present if not for my understanding.

when we come through difficult times it is easier to see how when one door closes another door opens, and if not for the door closing we would perhaps not have made the choice to move into that different, unplanned event or situation.

because of my spiritual connections and beliefs, it becomes destiny rather than chance…..however it may be due to one event taking place that another can happen… cosmically, perhaps mathematically, there is specific order rather than randomness to the individual events in one persons life. and if this is to be so, then does that require that all of the connections be of a similar specific order? the universe’s immensity is truly beyond our comprehension.

i am one who receives precognitive dreams….at times for the day, others years ahead. is this random? could i change the events if i knew that they were foretold to me? i tried it recently, and here is what happened:

flat tire dream — more than one flat tire several months ago. so when i saw that the tires were running on bald last month, i replaced all but one as it was okay, and i am on a very strict budget these days. remembering the dream, i thought that i was preventing it from coming true. a week after replacing the tires i had a flat with one of the new tires. when i took it to be repaired, they found that a honda key had been the cause ( i drive a nissan) and that it was not repairable. hum….. i think that there must be some order in life that we simply are not meant to understand, but look at events as road signs — okay you can pass GO now, proceed….

Was the wording of the question “Can a full understanding of the probability of certain outcomes help reduce anxiety?” facetious, or was the word “certain” used without recalling that it means 100% probability?

I’ve not yet had the pleasure of reading “The Drunkard’s Walk,” but I’m currently reading “The Black Swan” by Nassim Taleb, and am enjoying it. The two books appear to cover similar territory; it will be interesting to compare them.

I can recall a professor of mine speaking on the ‘chance’ of certain behaviors, based on a system of reward and punishment. This chance, or probability, that one behavior may be elicited over another was based upon learning the action of a behavior and its consequence. It is never, with absolute certainty, possible to know which behavior will be exhibited over another (with respect to human beings) as a result of conscious thought — the human has the ability to stop any action, think it through, and alter the behavior if it wishes (this is of course true only in instances absent of mental illness). You may only ever know a situations probability. After all, in the accounts of a particular behavior, is it not improperly performed at least once in its attempts of completion? The point is that numbers, and probability and statistics (or calculus for that!) are very much present in everyday thought, in addition to being used in the understanding of life and forward advancements.

My dad was a philosophy major in college. When I was a kid, we used to have lengthy discussions about free will versus determinism. For a long time I considered myself an existentialist…I surmised that we are condemned to be free, that we are each individually responsible for every detail of the unfolding of our lives. But as I got older, more and more seemed inherently out of my control. I began to sense that free will and determinism must be operating simultaneously, but my father insisted that you can’t have intermittent free will…it’s either all clockwork or all chaos, but not a little of each.

Then I learned about quantum physics, and about how the particles of everything around us are ultimately made up of mostly empty space held together by mysterious forces…forces that do not abide by the physical laws that govern large things. For all intents and purposes, quantum physics and classical physics cannot coexist…and yet they do. In fact, physicists are working around the clock to come up with a “grand unification theory”, a way to reconcile them.

To me, the free will/determinism dilemma is identical: determinism = classical physics, things abiding by predictable laws, and free will = renegade waves and particles appearing in two places at once, having non-local relationships, and otherwise working behind the scenes to make our reality appear to be made of something solid.

I’ve developed a hybrid philosophy i call “CHOOSE DETERMINISM” – it’s a sort of grand unification theory for philosophy. Maybe we CAN have a little of both. Maybe we have no choice…

As a conceptual artist, i’ve developed a couple of “philosoprops” to demonstrate these principles – one is a pair of dice that have three dots embossed on all sides. The roller has the sensation of free will, but the number will always come up on double 3’s. The other is an accompanying small propaganda-style booklet/questionnaire entitled “Are You a DETERMINIST? YOU DECIDE!” The reader is quizzed on just how much choice they’ve really had in life – and I hope they’ll be left with a feeling similar to the one left by your article – that relinquishing a false sense of control and choosing instead to find the positive in whatever happens is probably the best we can do.

The year before he broke Ruth’s record, Maris won the American League MVP award. He led the league in RBIs and hit 39 home runs. Not 61, of course, not even close. But in the first half of that year, he hit 27 home runs. And that was a 154 game seaon, with no expansion teams.

I saw one game that year(1960). The Yankees had a one run lead on Detroit in the top of the ninth. There were two outs. . The Tigers got a man on first, who was replaced with a pinch runner, who immediately stole second. The next batter hit a clean single to right. The runner, probably the fastest player the Tigers had, was running on the hit. I was in the right centerfield seats. I saw Maris move for the ball, on one hop, pivot and throw a perfect strike to Elston Howard who, in a split second tagged the runner out at the plate and win the game.

I lost my fear of flying by learning to fly. It had nothing to do with understanding the statistics (I did, from the beginning), but with repeated exposure to the experience. Probability and rationality are great, but familiarity is human.

Years ago, during my recovery from a back and neck injury caused by a bicycle accident, I was faced simultaneously with many forms of uncertainty: my husband had made it clear that marriage to someone with a physical limitation wasn’t his cup of tea; I had lost my job after being out sick for too long; my disability benefits were under fire due to political changes that carried down to agency levels; and I was simply terrified of having a handicap that would prevent me from working and being able to maintain the sort of independence I had come to take for granted.

I was lucky though, because many of my friends (including one very special woman who I met at the outpatient rehab treatment I received for six months) were apparently practicians of great level-headedness, and not at all into the superstitious drawing of (what i now realise are) post hoc connections that made up such a strong element of my formative years.
(I grew up in a predominantly Polish and Yugoslavian community, where there was no shortage of worry, forced down your throat if it didn’t come naturally to you…!)

One moment I will always remember (and which I still use as a sort of a mantra when I start to feel frustrated by my very human inability to see into the future) was during a short and choppy walk through a local park with the friend I’d met at the clinic.

I said to her, explaining my fear and anxiety, “You know, I can’t see the way ahead.” She was silent, and then looked at me, and after some time she smirked ever so slightly and said simply “How exciting!!”

And that’s what I remember now, when the Worries try to get me. It’s random. I grab my opportunities (I am reducing my dependency on physical therapy through special courses for back injuries, do Pilates twice a week, get acupuncture and respect my physical limitations.) and I’m happy to say that I am back at work, though very part time, and my divorce will soon be over. And I am looking forward to see how all these ‘bad things’ might work out!!

To Sandra of Cleveland: Many of my family were killed by the Nazis, but I often think, like the author, that I have Hitler to thank for growing up American. My mother would never have moved us to the United States without Hitler, and as a woman growing up in Germany, I would have never had the opportunities or the outlook to have the wonderful, varied, chancy life I’ve lived — and continue to live — as an American.

I’m tired of everybody demanding that their sensitivities be considered in stating one’s personal opinion. The author’s whole point is that events have unpredictable outcomes, and being happy that you had a good outcome from a bad event is definitely something you should do. Get over it.

In 1995 I played “eye tag” with my future husband on the subway in NYC. Over the next couple of days, I couldn’t help thinking about him–a complete stranger–a great deal, wondering if and where I might encounter him again. Four days later we ran into each other at the Metropolitan Museum. He was with someone else but managed to hand me his card. We hadn’t said a word to each other at this point.

I called him the next day. It turned out we both attended Rhode Island School of Design, but at different times. We knew a few people in common. Much later we figured out that we’d attended the same lecture by the artist Christo some 12 or thirteen years earlier.

Two more very strange coincidences kept us together (too complicated to explain here). Five years after we met, I left a tenured teaching position at a state university to be with him, and we married in 2002. Now I’m a poorly paid adjunct in NYC, but I’ve never looked back.

I’d always believed in chance and knew I’d benefited from it numerous times, especially when I was in my 20’s. Perhaps that was why I was willing to be open to that stranger who’s now my wonderful husband.

I’m so sorry about the members of your family who perished, but I don’t think that by “thank” Dr. Mlodinow meant gratitude. I took it in the figurative sense that we sometimes use it- cause and effect- as in, “I have polio to thank for this limp.” Or, “I suppose that I have a murderer to thank for my marriage- I met my wife while serving on the jury that convicted him.”

I took the whole passage to represent the unfathomable irony that good things can follow evil, and a chain of causation can be established later though it was never intended.

If Dr. Mlodinow can thank Hitler for his existence, my children can thank a patch of pavement outside Phoenix.

Six months ago I “celebrated” the 20th anniversary of a bicycle crash that left me with an epidural hematoma, a three night coma and a prescription for anti-seizure pills I will take every day for the rest of my life. When I say “celebrated,” I mean a party, a house full of friends.

It was a pivotal event that set much of the course of the rest of my life. Without it, a different chain of events would have followed that may have kept me from meeting the woman who became my wife and the mother of my children.

It was a horrible accident, a terrible thing to live through, but I celebrated the anniversary because it made me who I am, gave me the life I have. If I wish it had never happened, it would mean wishing I wasn’t the man I came to be, wishing I didn’t have the life I have, the children I love.

I should also add that I looked at the odds, the dangers, the risks, and got back on my bicycle four weeks after brain surgery. That was 120,000 miles + miles ago.

First, “I have Hitler to thank” does not really mean thanking Hitler. The ” were it not for the war” restates the same idea, but without the irony.
Second, better athletes have a better chance of setting records. Mickey Mantle was more likely to break Ruth’s single-season record than Maris.
Third, expectation does play a role in the likelihood of an event. Not so long after Roger Bannister broke the four-minute mile “barrier,” other runners, knowing that it could be done, followed suit.
Finally, I don’t think fear of air turbulence yields to a better understanding of the risk; I think it’s related to a need to feel in control. I have known for years that it is safer to fly than to drive, yet I have had periods in my life when turbulence was a white knuckle experience and other times when I could calmly reassure the fearful passenger next to me.
Cheers,
Gary McCardell

Its scary to consider what accidents we all are. Just think – one different sperm and you are not you. If your mother had had a headache that night…….

People seldom have a good understanding of statistics and coincidence. Rare events and coincidences will occur and the only meaningfulness behind them is that statistically it was predictable that something that rare would happen. In the meantime, we persistently worry about the wrong things. We worry about rare events and fail to worry about common events.

Seemingly random misfortune has also touched my life recently, and it has brought me some good effects as well. Just over a year ago and not yet 50, I was diagnosed with stage 3 appendix cancer (supposedly a 1-in-a-million occurrence), and have had two major surgeries and some serious complications from it. Nevertheless, I was incredibly fortunate to have it diagnosed at a relatively early stage, it’s more treatable than some other types of cancer, and I’m doing very well now. I used to wonder what it was that I did (or what it was in my genetic background, perhaps) that caused this disease, but it’s not something that’s likely to have an answer so it doesn’t worry me that much anymore. I’m very lucky to have excellent health care, a great job, and wonderful friends and family. Although I was previously a bit of a curmudgeon, my whole attitude has changed because of this disease. I have learned to set a really low bar for things that delight or satisfy me so that there’s something every day that I can reflect on with pleasure. Ten minutes of backyard bird-watching leaves me as happy as a two week vacation at the beach might. I don’t know what the future holds, I could be dead in two years or forty, but I don’t worry about it anymore. I just don’t want prolonged suffering, but one day at a time is the best way for me to take life now.

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The severe economic downturn has forced many people to reassess their values and the ways they act on them in their daily lives. For some, the pursuit of happiness, sanity, or even survival, has been transformed. Happy Days is a discussion about the search for contentment in its many forms — economic, emotional, physical, spiritual — and the stories of those striving to come to terms with the lives they lead.